Interest Rates, Corporate Bonds, and Mortgage-Backed Securities

A corporate treasurer prices a 10-year fixed-rate note at 5.5% yield to maturity (YTM) and the same maturity Treasury at 4.2%. The 130 bp spread compensates for default and liquidity. A pension fund buys a $50 million mortgage-backed security (MBS) pool yielding 5.8%, knowing the homeowners can refinance and hand back capital just when rates fall the most. The exam tests whether you can move between rate conventions, price duration and convexity correctly, decompose a corporate bond's spread, and understand why prepayment risk wrecks naive bond math on MBS.

A Treasury rate is a yield on U.S. government debt. Treasury bills make a single maturity payment, while notes and bonds generally pay coupons. A coupon bond's quoted yield summarizes all its cash flows; it is not automatically the zero rate for its maturity. Treasury yields also reflect liquidity and demand for safe collateral, so they need not equal secured funding rates of the same maturity.

A repurchase agreement (repo) combines a security sale today with an agreement to repurchase it later at a specified price, normally higher when the repo rate is positive.

Common mistakes

• Confusing Macaulay and modified duration. Macaulay is in years (weighted-average time). Modified is the price sensitivity (percent price change per 100 bp). They differ by the factor 1 + y/m. Trap: a question gives Macaulay 7.5 years and asks "% price change for a 50 bp rate rise." Wrong answer: 7.5 × 0.005 = 3.75%.
• Plugging semi-annual YTM into a continuous discount. A 6% YTM on a U.S. corporate is semi-annual; PV is $\sum CF_t / (1.03)^{2t}$. Plugging into $e^{-0.06 t}$ gives a different number. Trap: continuous-time models (Black-Scholes for bond options, FRM derivative chapters) need the rate converted first.
• Using duration alone for large rate moves. A 200 bp rate move on a 7-year duration bond: duration says -14% but actual move might be -12% due to positive convexity. Trap: given a 200 bp shock, the duration-only figure overstates the loss.

Bottom line

• Compounding conversion: $R_c = m \ln(1 + R_m / m)$. Continuous and discrete give the same PV but different rate quotes.
• Duration: Macaulay (years), Modified = Mac / (1 + y/m) (percent per 100 bp), Dollar = Modified × Price (× 0.0001 = dollars per bp). $\Delta P / P \approx -D_{\text{mod}} \Delta y$.
• Convexity: the second-order term improving the linear estimate, $\Delta P / P \approx -D \Delta y + \tfrac{1}{2} C (\Delta y)^2$; positive for vanilla bonds, negative for callable bonds and MBS.
• Term structure theories: pure expectations, liquidity preference (term premium), market segmentation, preferred habitat.

Exam shortcut

Memory aid: "Duration is the slope, convexity is the curve, prepayment cuts the curve short." Spread risk on a corporate is what changes daily; default risk is the binary tail. Both live inside the credit spread you observe.

The full lesson (about 7,957 words, 53 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.

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